I've been currently using Star CCM+'s ability to replace a mesh and map the solution to account for motion.

I created a VBA macro for Solidworks that generated all of my geometries automatically based on parameters of the problem.

Then I created a java macro that would open each one of the geometries in Star CCM+, create the mesh, and export the mesh.

Next I created a java macro that would first define paramaters of the problem (such as times step, number of iterations, etc.), iterate on one mesh, and then replace it with a new mesh for the next timestep.

For the problem I was solving the flow was caused by the motion of one flat plate relative to a stationary plate, so to account for this a field function was created that would define a volumetric source term based at each timestep.

I have compared my results to a first-order analytical solution, and the results agree very well.

Also, in the Java API there is something called Star Morpher, which makes references to moving meshes, but is not very well documented. If anybody has any idea how to use this I would be very interested in finding out how.